A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 20 per week at a price of $9 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 2 sales per week.

Question

(a) Find a function that models weekly profit in terms of price per feeder. (Let x be the price per feeder and P(x) be the profit.)

Answer 1

Let the number of $1 increases be n

selling price now : 9
number sold now: 20

after increase....
selling price = 9+n
number sold = 20-2n

P(n) = (9+n)(20-2n) - 5(20-2n)

( change my variable to x )